Research work of A. Mostowski in logical calculi

Abstract

This chapter discusses various research works of Andrzej Mostowski in logical calculi. Paper 16 introduces algebraic modeling for first order calculi. The main purpose of this paper is to outline a general method which permits to prove the intuitionistic non-deducibility of many formulas. The method consists in utilizing the connections between intuitionistic logic and the so-called Brouwerian lattices. Paper 59 deals with operators, which represent a natural generalization of logical quantifiers and formulate problems for those generalized quantifiers which correspond to the classical problems of first order logic. Paper 80 discusses the problem of axiomatizability. It proves the existence of complete sets of axioms and rules of inference for some many-valued predicate calculi without exhibiting them explicitly. Paper 85 discusses the generalization of two fundamental theorems concerning two-valued predicate calculus to the many-valued case. Paper 46 deals with problems which are specific for mathematics and solve them within the limits of mathematics alone and by applying mathematical methods only. Paper 89 is a collection of 16 lectures delivered at ·the Summer School in Vaasa, Finland, in 1964.